A. Tree Search

Codeforces

IDCF10100A

Time1000ms

Memory16MB

Difficulty—

English · Original

Formal · Original

You are given a tree with N nodes, each node has an associated cost. You need to answer M questions of the type: "which is the maximum cost of a path that contains node Q?". The first line of the input contains two integers N and M (1 ≤ N, M ≤ 100.000). The second line contains N integers representing the cost of the nodes ( - 20.000 ≤ cost ≤ 20.000). Each of the next N - 1 line contains two integers representing an edge between two nodes. On each of the next M lines there is a single integer Q corresponding to a question. The output should contain M lines. On line i print a single integer representing answer for the i-th question. ## Input The first line of the input contains two integers N and M (1 ≤ N, M ≤ 100.000). The second line contains N integers representing the cost of the nodes ( - 20.000 ≤ cost ≤ 20.000). Each of the next N - 1 line contains two integers representing an edge between two nodes. On each of the next M lines there is a single integer Q corresponding to a question. ## Output The output should contain M lines. On line i print a single integer representing answer for the i-th question. [samples]

**Definitions** Let $ N, M \in \mathbb{Z}^+ $ denote the number of nodes and queries, respectively. Let $ G = (V, E) $ be a tree with $ |V| = N $, $ |E| = N-1 $. Let $ c : V \to \mathbb{Z} $ be a cost function on nodes, with $ -20{,}000 \leq c(v) \leq 20{,}000 $. Let $ Q_1, \dots, Q_M \in V $ be the query nodes. **Constraints** 1. $ 1 \leq N, M \leq 100{,}000 $ 2. For all $ v \in V $, $ c(v) \in [-20{,}000, 20{,}000] $ 3. $ G $ is a connected acyclic undirected graph. **Objective** For each query $ Q_i $, compute: $$ \max_{\substack{P \subseteq V \\ P \text{ is a path in } G \\ Q_i \in P}} \sum_{v \in P} c(v) $$

API Response (JSON)

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